"When I install it into the new machine, will it be recognised as having 3 partitions." - yes, should do.
"Is there anything that need to be careful with?" - yes: 1. Make sure the jumper(s) of the 140Gb drive are set correctly in relation to the hard drive in the new PC, & 2. You don't void the warranty if you open the new PC's case &/or install new hardware. G